If f(x) `=X^(3) + ax^(2) +bx +c` has extreme values at x=-1 and x=3 . Find a,b,c.

Explanation

To solve the problem, we need to find the values of \( a \), \( b \), and \( c \) for the function \( f(x) = x^3 + ax^2 + bx + c \) given that it has extreme values at \( x = -1 \) and \( x = 3 \).

### Step 1: Differentiate the function
First, we differentiate the function \( f(x) \) to find its critical points:
\[ f'(x) = 3x^2 + 2ax + b \]

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